Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [statistics]

Mathematical statistics is the study of statistics from a mathematical standpoint, using probability theory and other branches of mathematics such as linear algebra and analysis.

Statistics is the science of the collection, organization, and interpretation of data. It deals with many aspects of data, which includes the planning of data collection in terms of the design of surveys and experiments. (From Wikipedia)

More specifically, mathematical statistics is the study of statistics from a mathematical standpoint, using probability theory as well as other branches of mathematics such as linear algebra and mathematical analysis. (From Wikipedia)

For questions which are more generally about collecting and treating data, it is advised that you post your question on Cross Validated and DSSE.

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Why is SSE called unexplained variation

Why is $$SSE=\sum(y-a-bx)^2$$ called the unexplained variation? I have real trouble understanding this concept which leads to the definition of the coefficient of determination. The books keep saying that the coefficient of determination is the…
David
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Determine similarity between atom distances in models

This is applied to bioinformatics, but I feel it is also a statistical question. I have the x,y,z coordinates of 392 atoms in a 392-atom molecule. There are 14 models of this molecule. In other words, 14 models of 392 x,y,z coordinates. For…
user84756
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Statistical dependency tests

I have a lots of football data for 2010 and I'm interested in finding the dependency of the number of average goals per game on a) the competition (e.g. Premiership, World Cup, FA cup) and b) the weather (e.g. sun, rain, snow etc). Note both are…
Daniel
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Combining classes in a multivariate hypergeometric distribution

Suppose I have a population of size $N$ made up of people of different U.S. political parties: $K_R$ Republicans, $K_D$ Democrats, $K_L$ Libertarians, $K_G$ Greens, $K_S$ Socialists and $K_I$ people with no political party (Independents), $K_R +…
psyllogism
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GPS coordinates statistics with rotated X & Y axis

I have a set of GPS coordinates along with their bearing angle. These coordinates are within 15 m of each other and so I can use cartesian math to determine the center, std deviation of coordinates etc. I am then trying to find a subset of GPS…
user110584
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Mean and Variance of Multiple Choice Exam

A Multiple choice exam has 100 questions, each with 5 possible answers. One mark is awarded for a correct answer and $\frac{1}{4}$ mark is deducted for an incorrect answer. A particular student has probability $p_{i}$ of knowing the correct answer…
Wendell Blatt
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Predicting data in many dimensions

I have two matrices deriving from one matrix of the original data. One is the training, the other is the validation set. Each matrix has rows= examples, columns = featuers. The proportions are 65% vs 35% respectively. Given that the data is in many…
user2827159
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How do I do a power calculation where the effect size and values of $\alpha$ and $\beta$ are known?

I am planning a study where the endpoint of the current practice is 40% successful. The null hypothesis will be rejected if the intervention produces a 60% success rate (treatment effect of interest). We are happy with a significance criterion of…
Sarah_C
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Poisson Distribution Lambda, Probability, and Looking for Exactly k

Automobiles arrive at a vehicle equipment inspection station according to a Poisson process with a rate of $ \lambda $ = 10 per hour. Suppose that with probability 0.5 an arriving vehicle will have no equipment violations. What is the probability…
Daniel Cazares
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how to interpret my confidence interval !

so we have to compare two categories , overweight to normal weighted persons and wanna know if the health risks for overweight are higher than normal people. (which logically overweight will have more health risks) minitab gives me this after…
emma
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If $\chi^2=0$ for a dataset, are the frequencies of the values in the contingency table all the same?

Could I say that if the $\chi^2$ value of a dataset is $0$, then the frequencies of the values of the cells in the contingency table are all the same? I have noticed that if I change the frequency of any of these values to be more than the other,…
Ted Flethuseo
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How to derive the marginal probability function of X?

Let $X$ and $Y$ be discrete random variables with joint probability function $f(x,y)=k\frac{2^(x+y)}{x!y!}$ for $x=0,1,2..$ and $y=0,1,2...$,where $k$ is a positive constant. The answer is $k\frac{(2^x)(e^2)}{x!}$. I do not know how to get the…
Jing
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Assume $Y_i=\beta x_{i} + \epsilon_{i}$ What is the variance of the LS estimator b?

So far I have $b=\frac{\sum_{i=1}^{n} x_{i}y_{i}}{\sum_{i=1}^{n} x_{i}^{2}}$ So I substituted for $Y_i$ and got $Var(b)=Var(\beta + \frac{\sum_{i=1}^{n} x_{i} \epsilon_{i}}{\sum_{i=1}^{n} x_{i}^{2}})$ But I got stuck after this and not sure how to…
Gamecocks99
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Statistics PDF problem

Let Xsub1, Xsub2, ..., Xsub48 be a random sample of size 48 from the distribution with pdf f(x) = 1/(x^2), 1 < x < infinity. Approximate the probability that at most 10 of these random variables have values greater than 4.
Fred
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least squares regression parabola

In my AP Stats course, we just finished our chapter on least squares regression lines and are moving on to non-linear regressions. I was expecting a least squares regression parabola, but instead we are using logs to make the function linear. I…
TAAPSogeking
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